The On-Line Encyclopedia of Integer Sequences (OEIS)

A259143 revision #13

A259143

Number of distinct digits needed to write the calendar date of n-th day of a non-leap year in decimal representation, without leading zeros.

1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

a(n) <= 4.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..365

Wikipedia, Calendar date

Index entries for sequences related to calendars

EXAMPLE

. | Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

. | 1 2 3 4 5 6 7 8 9 10 11 12

. ----+-------------------------------------------------

. 1 | 1 2 2 2 2 2 2 2 2 2 1 2

. 2 | 2 1 2 2 2 2 2 2 2 3 2 2

. 3 | 2 2 1 2 2 2 2 2 2 3 2 3

. 4 | 2 2 2 1 2 2 2 2 2 3 2 3

. 5 | 2 2 2 2 1 2 2 2 2 3 2 3

. 6 | 2 2 2 2 2 1 2 2 2 3 2 3

. 7 | 2 2 2 2 2 2 1 2 2 3 2 3

. 8 | 2 2 2 2 2 2 2 1 2 3 2 3

. 9 | 2 2 2 2 2 2 2 2 1 3 2 3

. 10 | 2 3 3 3 3 3 3 3 3 2 2 3

. 11 | 1 2 2 2 2 2 2 2 2 2 1 2

. 12 | 2 2 3 3 3 3 3 3 3 3 2 2

. 13 | 2 3 2 3 3 3 3 3 3 3 2 3

. 14 | 2 3 3 2 3 3 3 3 3 3 2 3

. 15 | 2 3 3 3 2 3 3 3 3 3 2 3

. 16 | 2 3 3 3 3 2 3 3 3 3 2 3

. 17 | 2 3 3 3 3 3 2 3 3 3 2 3

. 18 | 2 3 3 3 3 3 3 2 3 3 2 3

. 19 | 2 3 3 3 3 3 3 3 2 3 2 3

. 20 | 3 2 3 3 3 3 3 3 3 3 3 3

. 21 | 2 2 3 3 3 3 3 3 3 3 2 2

. 22 | 2 1 2 2 2 2 2 2 2 3 2 2

. 23 | 3 2 2 3 3 3 3 3 3 4 3 3

. 24 | 3 2 3 2 3 3 3 3 3 4 3 3

. 25 | 3 2 3 3 2 3 3 3 3 4 3 3

. 26 | 3 2 3 3 3 2 3 3 3 4 3 3

. 27 | 3 2 3 3 3 3 2 3 3 4 3 3

. 28 | 3 2 3 3 3 3 3 2 3 4 3 3

. 29 | 3 _ 3 3 3 3 3 3 2 4 3 3

. 30 | 3 _ 2 3 3 3 3 3 3 3 3 4

. 31 | 2 _ 2 _ 3 _ 3 3 _ 3 _ 3 .

13 days need just 1 digit: {1, 11, 33, 53, 62, 94, 125, 157, 188, 220, 252, 305, 315} = {Jan 1, Jan 11, Feb 2, Feb 22, Mar 3, Apr 4, May 5, Jun 6, Jul 7, Aug 8, Sep 9, Nov 1, Nov 11};

152 days need 2 digits: the first is the 2nd day = Jan 2, the last one is the 356th day = Dec 22;

192 days need 3 digits: the first is the 20th day = Jan 20, the last one is the last day of the year = Dec 31;

8 days need 4 digits: {296 .. 302, 364} = Oct 23 through Oct 29, and also the penultimate day of the year = Dec 30.

PROG

(Haskell)

import Data.List (nub)

a259143 n = a259143_list !! (n-1)

a259143_list = [length $ nub $ show m ++ show d |

m <- [1 .. 12], d <- [1 .. a008685 m]]

CROSSREFS

Cf. A008685.

Sequence in context: A055640 A098378 A160093 * A035931 A330634 A254524

Adjacent sequences: A259140 A259141 A259142 * A259144 A259145 A259146

KEYWORD

nonn,base,fini,full

AUTHOR

Reinhard Zumkeller, Jun 19 2015

STATUS

approved